Conventional geometric parameters of honeycombs (cell height, h, cell length, l, and cell angle, θ) have been used to find effective properties of honeycomb structures. However, these parameters appear to be difficult to control both a target shear stiffness (4 to 4.5 MPa) and a certain level of shear strain (˜10%) because the parameters are coupled to each other. A novel approach to design hexagonal honeycombs is suggested to be capable of controlling both shear stiffness and shear flexibility independently by defining two new parameters; effective height, R and horizontal separation, d. A numerical parametric study with commercial software, ABAQUS, is conducted using the two new parameters to investigate their affects on in-plane effective shear stiffness, G12*, and maximum shear strain, (γ12*)max of polycarbonate honeycombs under a fixed overall honeycomb height of 12.7 mm (0.5 in). The suggested approach is expected to be applied to design a light weight component requiring certain levels of shear stiffness and shear strain at the same time. For example, this component can be used as the shear layer for a shear band of a tire including those of the pneumatic, non-pneumatic and hybrid varieties.
The inventors are challenged with developing specialized materials that mimic elastomeric properties yet are composed of low dampening materials, thereby reducing energy loss under shear for use in the shear layer of a shear band of a tire. A solution may be found in a design of honeycombs. Our previous study on a design of shear flexure with honeycombs shows that cellular solids having negative Poisson's ratio, called auxetic, have high shear flexibility [Ju, J., Summers, J. d., Zigert, J., and Fadel, G, (2009), “Design of honeycomb meta-materials for high shear flexure,” In Proceedings of the ASME 2009 International Design Engineering Technical Conference, IDETC/CIE 2009, San Diego, Calif.].
The hexagonal honeycombs have been studied as a basic cellular structure. Since the pioneering work on the honeycomb mechanics by Gibson and Ashby [Gibson, L. J. and Ashby, M. F., (1997), Cellular Solids Structure and Properties, 2nd ed. Cambridge, UK: Cambridge University Press], many analytical and numerical models to describe in-plane effective properties of honeycombs are available in the literature; for example, a refined cell wall's bending model by adding a beam's stretching and hinging motion [Masters, I. G. and Evans, K. E., (1996), “Models for the Elastic Deformation of Honeycombs,” Composite Structures, vol. 35, no. pp. 403-22], a model with the energy method [Bezazi, A., Scarpa, F., and Remillat, C., (2005), “A Novel Centresymmetric Honeycomb Composite Structure,” Composite Structures, vol. 71, no. 536-64], a refined model with round shape at cell edges [Balawi, S. and Abot, J. L., (2008), “A Refined Model for the Effective in-Plane Elastic Moduli of Hexagonal Honeycombs,” Composite Structures, vol. 84, no. pp. 147-58], and a model using the homogenization method [Gonella, S. and Ruzzene, M., (2008), “Homogenization and Equivalent in-Plane Properties of Two Dimensional Periodic Lattices,” International Journal of Solid and Structures, vol. 45, no. pp. 2897-915]. In-plane mechanical properties with different cell types—square, hexagonal, triangle, mixed squares and triangles, diamond—were investigated by Wang and McDowell [Wang, A. J. and Mcdowell, D. L., (2004), “In-Plane Stiffness and Yield Strength of Periodic Metal Honeycombs,” Transactions of the ASME Journal of Engineering Materials and Technology, vol. 126, no. pp. 137-56]. Circular and chiral shapes of honeycombs have also been studied for a functional design [Chung, J. and Wass, A. M., (1999), “Compressive Response and Failure of Circular Cell Polycarbonate Honeycombs under in-Plane Uniaxial Stresses,” Transactions of the ASME Journal of Engineering Materials and Technology, vol. 121, no. pp. 494-502; Papka, S. and Kyriakides, S., (1998), “In-Plane Crushing of a Polycarbonate Honeycomb,” International Journal of Solid and Structures, vol. 35, no. pp. 239-67; Scarpa, F., Blain, S., Perrott, D., Ruzzene, M., and Yates, J. R., (2007), “Elastic Buckling of Hexagonal Chiral Cell Honeycombs,” Composites Part A, vol. 38, no. pp. 280-9]. A multifunctional approach requiring structural stability and fast heat transfer was investigated with honeycomb structures [Torquato, S., Gibiansky, L. V., Silva, M. J., and Gibson, L. J., (1998), “Effective Mechanical and Transport Properties of Cellular Solids,” International Journal of Mechanical Science, vol. 40, no. 1, pp. 71-82].
Compared to the fundamental studies on cellular solids, their practical applications have been limited to the development of stiff and ultra-light sandwich cores for aircraft and aerospace structures, which are related to the honeycombs' out of plane properties [Gellatry, R. A., Bijlaard, P. P., and Gallaherm, R. H., (1965), “Thermal Stress and Instability of Sandwich Cylinders on Rigid Supports,” Journal of Aircraft, vol. 2, no. 1, pp. 44-8; Lin, W., (1996), “The Point Force Response of Sandwich Panels and Its Application to Impact Problems,” in 37th Structures, Structural Dynamics, and Materials Conference, AIAA/ASME/ASCE/AHS/ASC, Salt Lake City, Utah April; Becker, W., (2000), “Closed-Form Analysis of the Thickness Effect of Regular Honeycomb Core Material,” Composite Structures, vol. 48, no. pp. 67-70; Kapania, R. K., Soliman, H. E., Vasudeva, S., Hughes, O., and Makjecha, D. P., (2008), “Static Analysis of Sandwich Panels with Square Honeycomb Core,” AIAA Journal vol. 46, no. 3, pp. 627-34; Abdelal, G. F. and Atef, A., (2008), “Thermal Fatigue Analysis of Solar Panel Structure for Micro-Satellite Applications,” International Journal of Mechanics and Materials in Design, vol. 4, no. pp. 53-62], and rigidified inflatable structure for housing [Khire, R. A., Dessel, S. V., Messac, A., and Mullur, A. A., (2006), “Study of a Honeycomb-Type Rigidified Inflatable Structure for Housing,” Journal of Structural Engineering, vol. 132, no. 10, pp. 1664-72]. Recently, honeycombs' in-plane flexibility began to be designed in aerospace morphing technology [Olympio, K. R. and Gandhi, F., (2007), “Zero-Nu Cellular Honeycomb Flexible Skins for One-Dimensional Wing Morphing,” in 48th Structures, Structural Dynamics, and Materials Conference, AIAA/ASME/ASCE/AHS/ASC, Honolulu, Hi. April 23-26; Bubert, E. A., Woods, B. K. S., Kothera, C. S., and Wereley, N. M., (2008), “Design and Fabrication of a Passive 1d Morphing Aircraft Skin,” in 49th Structures, Structural Dynamics, and Materials Conference, AIAA/ASME/ASCE/AHS/ASC, Schaumburg, Ill. April 7-10]. However, only limited practical studies on design with honeycomb configurations are available; for example, Seepersad et al. carried out a multifunctional design—structural and thermal in the application of gas turbine engines [Seepersad, C. C., Allen, J. K., Mcdowell, D. L., and Mistree, F., (2008), “Multifunctional Topology Design of Cellular Material Structures,” Journal of Mechanical Design, vol. 130, no. pp. 031404-13]. Huang and Gibson studied on the design of honeycombs for beam and plate structures [Huang, J. S. and Gibson, L. J., (1999), “Microstructural Design of Cellular Materials-l: Honeycomb Beams and Plates,” Acta Metallurgica et Materialia, vol. 43, no. pp. 1643-50]. The in-plane flexible design of honeycombs should be intensively studied for more structural functional applications.
Cellular materials are being considered to replace conventional materials such as polyurethane due to their lower densities, higher efficiencies under cyclic loading conditions, and their ability to be designed with specific mechanical properties. To be successful, the cellular material must have effective shear properties equaling those of polyurethane while reducing the affects of hysteretic energy loss. The material needs to have an effective shear modulus of between 4 and 4.5 MPa and must be able to withstand shear strains up to 10% before yielding occurs in the material. Additionally, the material needs to have an overall height of 12.7 mm and a length of 250 mm.
This application introduces a novel method for the design of honeycomb cellular structures to achieve two target effective properties simultaneously. In the design of honeycomb meso-structures, the conventional geometric parameters (cell height, h, cell length, l, and cell angle, θ) have been used to find effective properties of honeycomb structures. However, the use of these parameters can be cumbersome when designing for two effective properties at the same time. This paper introduces a new system for describing honeycomb structures which focuses on the geometric features of honeycombs which contribute to effective shear properties rather than direct geometric values.